After a collegiate career with the University of Denver during which he was named a First Team All-American, Grahame was signed by the Houston Aeros of the WHA. He played a season for the minor league Macon Whoopee in 1973 before coming up to the Aeros at the end of the season. In the 1974–75 season he made the Aeros for good, leading the WHA in wins, shutouts and goals against average and backstopping the club to the AVCO World Trophy, winning both the Ben Hatskin Trophy for best goaltender, First Team All-Star accolades and the WHA Playoff MVP. His following two seasons saw an equal degree of success, including a Second Team All-Star berth in 1976 and a second Hatskin award in 1977.